document.write( "Question 1092649: I need a little help on my homework. I tried them all and I know some of them are right i just have a question on a few because if i can understand those problems the ones similar I can do. So we are learning about how to solve inequalities and graphing them on a number line. I started this one but need a little help finishing it.
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\n" ); document.write( "\n" ); document.write( "/x/>x-1, and i need 2 inequalities. i have the first which is x>x-1 but i don't have the other one and is not quite such how to solve either one and my other one is
\n" ); document.write( "7-/2x/>5, I have both the inequalities and answers (x>-6; x<6) i just don't know how to put on the third number line because my teacher said something about the union?
\n" ); document.write( "Can you help? That would be appreciative? \n" ); document.write( "

Algebra.Com's Answer #707283 by ikleyn(52776) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "The folk wisdom says: It is better to see once, than to hear 100 times.\r
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\n" ); document.write( "\n" ); document.write( "Plots y = |x| (red) and y = x-1 (green)\r
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\n" ); document.write( "\n" ); document.write( "The answer to the first your inequality is: the solution is the set of ALL real numbers.\r
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\n" ); document.write( "Solution to the first inequality\r
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\n" ); document.write( "\n" ); document.write( "|x| > x - 1.\r
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document.write( "We must re-write this inequality separately for x >= 0  and for  x < 0,  where the expressions for |x| are different.\r\n" );
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document.write( "1.  For x >= 0  you have  |x| = x.  Then the original inequality takes the form \r\n" );
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document.write( "    x > x - 1.     (1)\r\n" );
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document.write( "    This inequality is true for all values of x. \r\n" );
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document.write( "    Thus in the domain  x >= 0  the solution for (1), and, hence, for the original inequality is the set  [0,infinity).\r\n" );
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document.write( "2.  For  x < 0 you have  |x| = -x.  Then the original inequality takes the form \r\n" );
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document.write( "    -x > x - 1.     (2)\r\n" );
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document.write( "     or, equivalently,\r\n" );
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document.write( "     2x < 1.     ( I hope you know elementary operations with inequalities, so\r\n" );
document.write( "                   such transformations should be clear to you . . . )\r\n" );
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document.write( "     It implies  x < 1/2,  which ALWAYS is true in the domain  x < 0.\r\n" );
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document.write( "     So, in the domain  x < 0 the solution set for (2), and, hence, for the original inequality is the set  (-infinity,0).\r\n" );
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document.write( "3.  Conclusion.  The solution set for the original equation is the entire number line.\r\n" );
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